|
%I #4 Oct 02 2023 10:54:06
%S 1,137,18769,2571353,352275494,48261760899,6611863739440,
%T 905825674293229,124098164230813075,17001454918435590842,
%U 2329200203203553290874,319100548313701481849195
%N Expansion of 1/(1 - 137 x - 133 x^4).
%C From characteristic polynomial of the matrix: {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {133, 0, 0, 137}}.
%C Polynomial base is Pisot and the large positiuve root is near 1/alpha: 137.00005172368373...
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (137, 0, 0, 133).
%F a(n) =Expansion(1/(1 - 137 x - 133 x^4))
%t mc = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {133, 0, 0, 137}}; f[x_] = CharacteristicPolynomial[mc, x]; g[x_] = Expand[x^4*f[1/x]]; Table[ SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]
%K nonn
%O 1,2
%A _Roger L. Bagula_, Jan 29 2008
|
